Partially hyperbolic diffeomorphisms with compact centerfoliations

Andrey Gogolev

doi:10.3934/jmd.2011.5.747

Article Contents

2011, Volume 5, Issue 4: 747-769. Doi: 10.3934/jmd.2011.5.747

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Partially hyperbolic diffeomorphisms with compact center foliations

Andrey Gogolev^1,

1.
Department ofMathematical Sciences, The State University of New York, Binghamton, NY 13902

Received: November 2011

Revised: February 2012

Published: February 2012

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Abstract

Let $f\colon M\to M$ be a partially hyperbolic diffeomorphism such that all of its center leaves are compact. We prove that Sullivan's example of a circle foliation that has arbitrary long leaves cannot be the center foliation of $f$. This is proved by thorough study of the accessible boundaries of the center-stable and the center-unstable leaves.
Also we show that a finite cover of $f$ fibers over an Anosov toral automorphism if one of the following conditions is met:

1. the center foliation of $f$ has codimension 2, or
2. the center leaves of $f$ are simply connected leaves and the unstable foliation of $f$ is one-dimensional.

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Mathematics Subject Classification: Primary: 37D30, 57R30; Secondary: 37D20.

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